MinT - Information on Result #1014908

Information on Result #1014908

Linear OOA(8¹⁶⁰, 699088, F₈, 3, 23) (dual of [(699088, 3), 2097104, 24]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁹, 35, F₈, 3, 11) (dual of [(35, 3), 86, 12]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 19, 35)-net over F₈, using
  - net from sequence [i] based on digital (8, 34)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 7, N(F)Â =Â 34, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using a function field by SÃ©mirat [i]
linear OOA(8¹⁴¹, 699053, F₈, 3, 23) (dual of [(699053, 3), 2097018, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹⁴¹, 2097159, F₈, 23) (dual of [2097159, 2097018, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
    1. linear OA(8¹⁴¹, 2097152, F₈, 23) (dual of [2097152, 2097011, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(8¹³⁴, 2097152, F₈, 22) (dual of [2097152, 2097018, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.